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Bulletin of the London Mathematical Society Advance Access originally published online on November 16, 2007
Bulletin of the London Mathematical Society 2007 39(6):921-928; doi:10.1112/blms/bdm081
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© 2007 London Mathematical Society

Extremal mean width when covering the 1-skeleton

Károly J. Böröczky

Alfréd Rényi Institute of Mathematics
PO Box 127
H–1364, Budapest
Hungary
and
Department of Geometry
Roland Eötvös University
Pázmány Péter sétány 1/C
H–1117, Budapest
Hungary

Gergely Wintsche

Teacher Training Department
Roland Eötvös University
Pázmány Péter sétány 1/C
H–1117, Budapest
Hungary
wgerg@ludens.elte.hu

Received 10 January 2006. Revision received 26 April 2007.

For a given convex body K in Rd, let Dn be the compact convex set of maximal mean width whose 1-skeleton can be covered by n congruent copies of K. Based on the fact that the mean width is proportional to the average perimeter of two-dimensional projections, it is proved that Dn is close to being a segment for large n.

Dedicated to Imre Bárány on occasion of his sixtieth birthday

2000 Mathematics Subject Classification 52C17, 52A22, 52A39.

First author supported by OTKA grants 043520 and 049301, and the EU Marie Curie project DiscConvGeo.


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